Fano resonances as a probe of phase coherence in quantum dots

In the presence of direct trajectories connecting source and drain contacts, the conductance of a quantum dot may exhibit resonances of the Fano type. Since Fano resonances result from the interference of two transmission pathways, their lineshape (as described by the Fano parameter q) is sensitive to dephasing in the quantum dot. We show that under certain circumstances the dephasing time can be extracted from a measurement of q for a single resonance. We also show that q fluctuates from level to level, and calculate its probability distribution for a chaotic quantum dot. Our results are relevant to recent experiments by Goeres et al.Comment: 4 pages, 3 figures; published versio

Shot Noise in SU(N) Quantum Dot Kondo Effects

We study shot noise in the current of quantum dots whose low-energy behaviour corresponds to an SU(N) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. For general N, two-particle Fermi liquid interactions have two distinct effects: they can enhance the noise via back-scattering processes with an N-dependent effective charge, and can also modify the coherent partition noise already present without interactions. For N=4, in contrast to the SU(2) case, interactions enhance shot noise solely through an enhancement of partition noise. This leads to a non-trivial prediction for experiment.Comment: 4+ pages; error in numerical prefactor describing interaction effect on noise correcte

Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers

Mechanical Entanglement via Detuned Parametric Amplification

We propose two schemes to generate entanglement between a pair of mechanical oscillators using parametric amplification. In contrast to existing parametric drive-based protocols, both schemes operate in the steady-state. Using a detuned parametric drive to maintain equilibrium and to couple orthogonal quadratures, our approach can be viewed as a two-mode extension of previous proposals for parametric squeezing. We find that robust steady-state entanglement is possible for matched oscillators with well-controlled coupling. In addition, one of the proposed schemes is robust to differences in the damping rates of the two oscillators.Comment: 13 pages, 2 figure

Detuned Mechanical Parametric Amplification as a Quantum Non-Demolition Measurement

Recently it has been demonstrated that the combination of weak-continuous position detection with detuned parametric driving can lead to significant steady-state mechanical squeezing, far beyond the 3 dB limit normally associated with parametric driving. In this work, we show the close connection between this detuned scheme and quantum non-demolition (QND) measurement of a single mechanical quadrature. In particular, we show that applying an experimentally realistic detuned parametric drive to a cavity optomechanical system allows one to effectively realize a QND measurement despite being in the bad-cavity limit. In the limit of strong squeezing, we show that this scheme offers significant advantages over standard backaction evasion, not only by allowing operation in the weak measurement and low efficiency regimes, but also in terms of the purity of the mechanical state.Comment: 17 pages, 2 figure

ERK1/2 signaling dominates over RhoA signaling in regulating early changes in RNA expression induced by endothelin-1 in neonatal rat cardiomyocytes

Cardiomyocyte hypertrophy is associated with changes in gene expression. Extracellular signal-regulated kinases 1/2 (ERK1/2) and RhoA [activated by hypertrophic agonists (e.g. endothelin-1)] regulate gene expression and are implicated in the response, but their relative significance in regulating the cardiomyocyte transcriptome is unknown. Our aim was to establish the significance of ERK1/2 and/or RhoA in the early cardiomyocyte transcriptomic response to endothelin-1.Cardiomyocytes were exposed to endothelin-1 (1 h) with/without PD184352 (to inhibit ERK1/2) or C3 transferase (C3T, to inhibit RhoA). RNA expression was analyzed using microarrays and qPCR. ERK1/2 signaling positively regulated approximately 65% of the early gene expression response to ET-1 with a small (approximately 2%) negative effect, whereas RhoA signaling positively regulated approximately 10% of the early gene expression response to ET-1 with a greater (approximately 14%) negative contribution. Of RNAs non-responsive to endothelin-1, 66 or 448 were regulated by PD184352 or C3T, respectively, indicating that RhoA had a more significant effect on baseline RNA expression. mRNAs upregulated by endothelin-1 encoded a number of receptor ligands (e.g. Ereg, Areg, Hbegf) and transcription factors (e.g. Abra/Srf) that potentially propagate the response.ERK1/2 dominates over RhoA in the early transcriptomic response to endothelin-1. RhoA plays a major role in maintaining baseline RNA expression but, with upregulation of Abra/Srf by endothelin-1, RhoA may regulate changes in RNA expression over longer times. Our data identify ERK1/2 as a more significant node than RhoA in regulating the early stages of cardiomyocyte hypertrophy

Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion

We present a fully quantum theory describing the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the opto-mechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.Comment: 5 pages, 2 figure

Quantum master equation descriptions of a nanomechanical resonator coupled to a single-electron transistor

We analyse the quantum dynamics of a nanomechanical resonator coupled to a normal-state single-electron transistor (SET). Starting from a microscopic description of the system, we derive a master equation for the SET island charge and resonator which is valid in the limit of weak electro-mechanical coupling. Using this master equation we show that, apart from brief transients, the resonator always behaves like a damped harmonic oscillator with a shifted frequency and relaxes into a thermal-like steady state. Although the behaviour remains qualitatively the same, we find that the magnitude of the resonator damping rate and frequency shift depend very sensitively on the relative magnitudes of the resonator period and the electron tunnelling time. Maximum damping occurs when the electrical and mechanical time-scales are the same, but the frequency shift is greatest when the resonator moves much more slowly than the island charge. We then derive reduced master equations which describe just the resonator dynamics. By making slightly different approximations, we obtain two different reduced master equations for the resonator. Apart from minor differences, the two reduced master equations give rise to a consistent picture of the resonator dynamics which matches that obtained from the master equation including the SET island charge.Comment: 22 pages, 4 figure